DESCRIPTION: Until recently a cure for HIV did not seem possible. However, recent developments suggest that some patients have been cured or demonstrate post-treatment control (PTC) of viremia to undetectable levels, corresponding to a functional cure. Further, there are important new ideas on how to safely activate the HIV-1 latent reservoir, which is believed to be the main obstacle to HIV-1 eradication from a patient. To advance the goal of cure we need to understand these recent clinical observations in quantitative detail. This grant aims to address this gap in knowledge, by leveraging the power of mathematical modeling to understand the dynamics of PTC and activation of the latent reservoir, to compare different biological mechanisms at play in those phenomena and to propose new protocols to advance the HIV cure agenda. We also propose to use mathematical modeling to advance the cure agenda for another chronic infection, hepatitis C virus (HCV). Our hypotheses are: i) that patients whose latent reservoir decays to sufficiently small levels on treatment are more likely to exhibit PTC, and thus we will develop models to understand the biological and dynamic processes that link latency and PTC; ii) that analyzing viral and infected cell kinetics under new therapeutic protocols aiming at activating latently infected cells will lead to new insights into hw to reduce or eliminate this reservoir, and thus we propose to develop a quantitative understanding of these therapies by modeling clinical trial data; iii) that by modeling the effects of new potent direct-acting antivirals for HCV, which target specific viral proteins and have multiple synergistic effects, we will be able to help design the potent drug combinations that are necessary for HCV cure. Altogether, our objectives are to assist clinical collaborators in studies involving HIV (as well as HCV) whenever we feel that rigorous analysis can lead to new insights or to improved treatments for patients. These studies may also raise interesting theoretical questions and drive future modeling efforts.